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Hölder estimates and large time behavior for a nonlocal doubly nonlinear evolution
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4309-9242
2016 (English)In: Analysis & PDE, ISSN 2157-5045, E-ISSN 1948-206X, Vol. 9, no 6, p. 1447-1482Article in journal (Refereed) Published
Abstract [en]

The nonlinear and nonlocal PDE vertical bar nu(t)vertical bar(p-2) nu(t) + (-Delta p)(s)nu = 0, where (-Delta(p))(s) v(x,t) = 2 P.V. integral(Rn) vertical bar nu(x,t) - nu(x+y,t)vertical bar(p-2)nu(x,t)-nu(x,y,t))/vertical bar y vertical bar(n+sp) dy; has the interesting feature that an associated Rayleigh quotient is nonincreasing in time along solutions. We prove the existence of a weak solution of the corresponding initial value problem which is also unique as a viscosity solution. Moreover, we provide Hlder estimates for viscosity solutions and relate the asymptotic behavior of solutions to the eigenvalue problem for the fractional p-Laplacian.

Place, publisher, year, edition, pages
Mathematical Sciences Publishers , 2016. Vol. 9, no 6, p. 1447-1482
Keywords [en]
doubly nonlinear evolution, Holder estimates, eigenvalue problem, fractional p-Laplacian, nonlocal equation
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-200043DOI: 10.2140/apde.2016.9.1447ISI: 000389831600006Scopus ID: 2-s2.0-84992724068OAI: oai:DiVA.org:kth-200043DiVA, id: diva2:1068806
Funder
Swedish Research Council, 2012-3124
Note

QC 20170126

Available from: 2017-01-26 Created: 2017-01-20 Last updated: 2017-11-29Bibliographically approved

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Lindgren, Erik

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  • apa
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  • de-DE
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  • nn-NB
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  • Other locale
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Output format
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